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New Trends in the Theory of Hyperbolic Equations

New Trends in the Theory of Hyperbolic Equations
Author: Michael Reissig
Publisher: Springer Science & Business Media
Total Pages: 520
Release: 2006-03-21
Genre: Mathematics
ISBN: 3764373865

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Presenting several developments in the theory of hyperbolic equations, this book's contributions deal with questions of low regularity, critical growth, ill-posedness, decay estimates for solutions of different non-linear hyperbolic models, and introduce new approaches based on microlocal methods.


Operator Theory and Indefinite Inner Product Spaces

Operator Theory and Indefinite Inner Product Spaces
Author: Matthias Langer
Publisher: Birkhäuser
Total Pages: 381
Release: 2006-06-16
Genre: Mathematics
ISBN: 9783764375164

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A colloquium on operator theory was held in Vienna, Austria, in March 2004, on the occasion of the retirement of Heinz Langer, a leading expert in operator theory and indefinite inner product spaces. The book contains fifteen refereed articles reporting on recent and original results in various areas of operator theory, all of them related with the work of Heinz Langer. The topics range from abstract spectral theory in Krein spaces to more concrete applications, such as boundary value problems, the study of orthogonal functions, or moment problems. The book closes with a historical survey paper.


Hyperbolic Conservation Laws in Continuum Physics

Hyperbolic Conservation Laws in Continuum Physics
Author: Constantine M. Dafermos
Publisher: Springer Science & Business Media
Total Pages: 636
Release: 2006-01-16
Genre: Mathematics
ISBN: 3540290893

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This is a lucid and authoritative exposition of the mathematical theory of hyperbolic system laws. The second edition contains a new chapter recounting exciting recent developments on the vanishing viscosity method. Numerous new sections introduce newly derived results. From the reviews: "The author is known as one of the leading experts in the field. His masterly written book is, surely, the most complete exposition in the subject of conservations laws." --Zentralblatt MATH


Partial Differential and Integral Equations

Partial Differential and Integral Equations
Author: Heinrich Begehr
Publisher: Springer Science & Business Media
Total Pages: 388
Release: 1999
Genre: Mathematics
ISBN: 9780792354826

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Recent results on partial differential equations as well as with complex analytic methods on singular integral equations and on related subjects are presented. Many of the contributions are survey articles. Topics ranging from elliptic, parabolic, hyperbolic, and mixed-type equations and systems to hyper-complex and quatern ionic analysis, M-analytic, bianalytic, polyharmonic and functions of several complex variables are covered. Applications to mathematical physics are also included. Audience: Specialists in partial differential equations and related topics, with an interest in real and complex methods and in applications to mathematical physics will find this book very useful.


Progress in Partial Differential Equations

Progress in Partial Differential Equations
Author: Michael Reissig
Publisher: Springer Science & Business Media
Total Pages: 448
Release: 2013-03-30
Genre: Mathematics
ISBN: 3319001256

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Progress in Partial Differential Equations is devoted to modern topics in the theory of partial differential equations. It consists of both original articles and survey papers covering a wide scope of research topics in partial differential equations and their applications. The contributors were participants of the 8th ISAAC congress in Moscow in 2011 or are members of the PDE interest group of the ISAAC society. This volume is addressed to graduate students at various levels as well as researchers in partial differential equations and related fields. The readers will find this an excellent resource of both introductory and advanced material. The key topics are: • Linear hyperbolic equations and systems (scattering, symmetrisers) • Non-linear wave models (global existence, decay estimates, blow-up) • Evolution equations (control theory, well-posedness, smoothing) • Elliptic equations (uniqueness, non-uniqueness, positive solutions) • Special models from applications (Kirchhoff equation, Zakharov-Kuznetsov equation, thermoelasticity)


Hyperbolic Problems: Theory, Numerics And Applications (In 2 Volumes)

Hyperbolic Problems: Theory, Numerics And Applications (In 2 Volumes)
Author: Tatsien Li
Publisher: World Scientific
Total Pages: 793
Release: 2012-09-28
Genre: Mathematics
ISBN: 9814417106

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This two-volume book is devoted to mathematical theory, numerics and applications of hyperbolic problems. Hyperbolic problems have not only a long history but also extremely rich physical background. The development is highly stimulated by their applications to Physics, Biology, and Engineering Sciences; in particular, by the design of effective numerical algorithms. Due to recent rapid development of computers, more and more scientists use hyperbolic partial differential equations and related evolutionary equations as basic tools when proposing new mathematical models of various phenomena and related numerical algorithms.This book contains 80 original research and review papers which are written by leading researchers and promising young scientists, which cover a diverse range of multi-disciplinary topics addressing theoretical, modeling and computational issues arising under the umbrella of ';Hyperbolic Partial Differential Equations';. It is aimed at mathematicians, researchers in applied sciences and graduate students.


Mathematical Analysis, Probability and Applications – Plenary Lectures

Mathematical Analysis, Probability and Applications – Plenary Lectures
Author: Tao Qian
Publisher: Springer
Total Pages: 335
Release: 2016-08-25
Genre: Mathematics
ISBN: 3319419455

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This book collects lectures given by the plenary speakers at the 10th International ISAAC Congress, held in Macau, China in 2015. The contributions, authored by eminent specialists, present some of the most exciting recent developments in mathematical analysis, probability theory, and related applications. Topics include: partial differential equations in mathematical physics, Fourier analysis, probability and Brownian motion, numerical analysis, and reproducing kernels. The volume also presents a lecture on the visual exploration of complex functions using the domain coloring technique. Thanks to the accessible style used, readers only need a basic command of calculus.


Well-posedness of Linear Hyperbolic Problems

Well-posedness of Linear Hyperbolic Problems
Author: Aleksandr Mikhaĭlovich Blokhin
Publisher: Nova Publishers
Total Pages: 178
Release: 2006
Genre: Mathematics
ISBN: 9781594549762

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"This book will be useful for students and specialists of partial differential equations and the mathematical sciences because it clarifies crucial points of Kreiss' symmetrizer technique. The Kreiss technique was developed by H.O. Kreiss for initial boundary value problems for linear hyperbolic systems. This technique is important because it involves equations that are used in many of the applied sciences. The research presented in this book takes unique approaches to exploring the Kreiss technique that will add insight and new perspectives to linear hyperbolic problems"--Publ. web site.


More Progresses In Analysis - Proceedings Of The 5th International Isaac Congress

More Progresses In Analysis - Proceedings Of The 5th International Isaac Congress
Author: Heinrich G W Begehr
Publisher: World Scientific
Total Pages: 1497
Release: 2009-05-12
Genre: Mathematics
ISBN: 9814469688

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International ISAAC (International Society for Analysis, its Applications and Computation) Congresses have been held every second year since 1997. The proceedings report on a regular basis on the progresses of the field in recent years, where the most active areas in analysis, its applications and computation are covered. Plenary lectures also highlight recent results. This volume concentrates mainly on partial differential equations, but also includes function spaces, operator theory, integral transforms and equations, potential theory, complex analysis and generalizations, stochastic analysis, inverse problems, homogenization, continuum mechanics, mathematical biology and medicine. With over 350 participants attending the congress, the book comprises 140 papers from 211 authors.The volume also serves for transferring personal information about the ISAAC and its members. This volume includes citations for O Besov, V Burenkov and R P Gilbert on the occasion of their anniversaries.